A takes 2 hours more than B to cover a distance of 40 km. If A doubles his speed, he takes $1\frac{1}{2}$ hour more than B to cover 80 km. To cover a distance of 120 km, how much time(in hours) will B take travelling at his same speed?
Answer & explanation
Correct answer: option 4
Let speed of B = S km/h
Time taken by B to cover 40km = \(\frac{40}{S}\)
Time taken by A = \(\frac{40}{S}\) + 2
Now , Distance = 80 km
Time taken by B to cover 80 km = \(\frac{80}{S}\) --------(2)
Speed of A when he double his speed = \(\frac{40S}{20 + S}\)
Time taken by A to cover 80 km = \(\frac{40 + 2S}{S}\) ------(3)
Subtracting (2) from (3) ,
\(\frac{40 + 2S}{S}\) - \(\frac{80}{S}\) = \(\frac{3}{2}\)
2 ( 40 + 2S - 80) = 3S
4S - 80 = 3S
S = 80
Speed of B = 80 km/h
Distance = 120 km
Time taken by B = \(\frac{120}{80}\)
So , Time taken by B to cover 90 km is 1\(\frac{1}{2}\) hours.